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m_a_m_a [10]
1 year ago
9

Factor completely 4x^2 − 32

Mathematics
1 answer:
Blababa [14]1 year ago
4 0

Answer: 4(x+2\sqrt{2})(x-2\sqrt{2})

Step-by-step explanation:

We can first take out the common factor of 4, as both 4x² and -32 are divisible by 4.

4(x^2-8)

From here, we can assume that x²-8 is a difference of two squares even though 8 is not a perfect square.

<em>For review, a difference of two squares </em>a^2-b^2 can be factored into (a+b)(a-b).

4(x^2-8)\\4(x+\sqrt{8})(x-\sqrt{8})\\4(x+2\sqrt{2})(x-2\sqrt{2})

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Match the term with the definition.
marta [7]
1A
2D
3B
4C
5E

Hope this helps!
3 0
3 years ago
Use the empirical rule to solve the problem. The annual precipitation for one city is normally distributed with a mean of 288 in
nadezda [96]

Answer:

z=-1.99

z=1.99

And if we solve for a we got

a=288 -1.99*3.7=214.4

a=288 +1.99*3.7=295.4

And the limits for this case are: (214.4; 295.4)

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the annual precipitation of a population, and for this case we know the distribution for X is given by:

X \sim N(288,3.7)  

Where \mu=288 and \sigma=3.7

The confidence level is 95.44 and the signficance is 1-0.9544=0.0456 and the value of \alpha/2 =0.0228. And the critical value for this case is z = \pm 1.99

Using this condition we can find the limits

z=-1.99

z=1.99

And if we solve for a we got

a=288 -1.99*3.7=214.4

a=288 +1.99*3.7=295.4

And the limits for this case are: (214.4; 295.4)

8 0
3 years ago
6. An urn contains 15 red balls and 8 blue balls. In each draw, one ball is extracted at random. It is then returned to the urn,
Leviafan [203]

Answer:

P(C4) = 0.0711

Step-by-step explanation:

consider the first draw = 15/23  since it cannot be a blue ball

The second draw = 21/29 since 6 more red balls will be added after the draw since a blue ball cannot be drawn

the third draw = 27/35 since 6 more red balls will be added after each draw since a blue ball cannot be drawn

therefore the total number of red balls will be = 15 + 6 + 6 + 6 = 33 red balls after the 4th draw. the total ball now in the urn= 33 red + 4 blue = 41

Hence the probability of drawing a blue ball at the fourth draw after drawing red balls at the previous attempts = 8/41

P(C4) = P ( fourth ball is blue ) * P( first ball red)*P(second ball red) *P(third ball red )

= (8/41) * (15/23) * (21/29)* (27/35) = 0.0711

8 0
3 years ago
One liter of paint covers 100 square feet. How many gallons of paint does it take to cover a room whose walls have an area of 80
mezya [45]
1 gallon is 3.78 L
100 sq feet needs 1 L
800 sq feet needs x

100/800 = 1/x
100x = 800
x = 800/100
x = 8 L

If you use the fact that 4 L = 1 gallon then you need 2 gallons of paint. I you use the more accurate 3.78 L then
1 gallon = 3.78 L
x gallon = 8 L

3.78 x = 8*1
x = 8/3.78
x = 2.12 gallons.
 
I guess you could say that 1 gallon and 1 L would do you.
8 0
2 years ago
Can you answer these questions I need them today 10 points if you do
quester [9]
#1.) A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers. The number 8 is a rational number because it can be written as the fraction 8/1.

I don't want to give you the answer cause that will not help you I'm the future If I just give it to you. It might help you but that's what I learned in school is that it doesn't help. Because like if you cheat on a test you won't get to learn. But if you did it yourself and got it wrong you can see why
4 0
3 years ago
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